symmetric relation

let $\text{[math]}$ be a relation over set $\text{[math]}$ ( $\text{[math]}$ )
a relation is symmetric if for each $\text{[math]}$ , if $\text{[math]}$ then $\text{[math]}$ (if $\text{[math]}$ then $\text{[math]}$ )

$\text{[math]}$

$\text{[math]}$ symmetric $\text{[math]}$ there exists $\text{[math]}$ so that $\text{[math]}$

the matrix that represents such relations has the property $\text{[math]}$ , e.g.
src_sage{ld(matrix(3, [0,1,0, 1,0,0, 0,0,0]))} {{{results( $\text{[math]}$ )}}}